reserve w, w1, w2 for Element of ExtREAL;
reserve c, c1, c2 for Complex;
reserve A, B, C, D for complex-membered set;
reserve F, G, H, I for ext-real-membered set;
reserve a, b, s, t, z for Complex;
reserve f, g, h, i, j for ExtReal;
reserve r for Real;
reserve e for set;

theorem Th200:
  a <> 0 implies a ** (A\+\B) = (a**A) \+\ (a**B)
proof
  assume
A1: a <> 0;
  thus a ** (A \+\ B) = (a**(A\B)) \/ (a**(B\A)) by Th92
    .= ((a**A)\(a**B)) \/ (a**(B\A)) by A1,Th199
    .= (a**A) \+\ (a**B) by A1,Th199;
end;
